High intensity electrical discharge machines are being built or developed which are capable of producing electrical pulses having currents of from about 100,000 to greater than 1,000,000 amperes at voltages of from about 100,000 volts to greater than 20,000,000 volts. Such electrical pulses may be used to produce electron beams which in turn may be utilized to provide interactions with gases or other materials for use in materials studies, testing of deposition of high energy in materials, production of various radiations, or for similar purposes. Various electrical discharge devices, such as diodes and the like, are often connected to these machines and utilized to produce a particular electron beam discharge to effect some one or more of the above described uses. One such device utilizes concentric tubular electrodes to produce a radially converging electron beam discharge to irradiate a cylindrical-shaped volume. Many of these discharge devices, it has been found, are limited as to the total current which may be carried by the anode and the peak voltage which may be produced and brought to bear in the device to provide a desired use. These devices are often limited in these respects by factors that are inherent in the design or configuration of the device. Some of these limitations may include magnetron capture mechanism, preferential emission from the cathode ends, and azimuthal asymmetry in current density as well as voltage breakdowns across insulator surfaces in the anode-cathode region of the discharge device.